Spectral methods for circuit analysis

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 119-124).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Harmonic balance (HB) methods are frequency-domain algorithms used for high accuracy computation of the periodic steady-state of circuits. Matrix-implicit Krylov-subspace techniques have made it possible for these methods to simulate large circuits more efficiently. However, the harmonic balance methods are not so efficient in computing steady-state solutions of strongly nonlinear circuits with rapid transitions. While the time-domain shooting-Newton methods can handle these problems, the low-order integration methods typically used with shooting-Newton methods are inefficient when high solution accuracy is required. We first examine possible enhancements to the standard state-of-the-art preconditioned matrix-implicit Krylovsubspace HB method. We formulate the BDF time-domain preconditioners and show that they can be quite effective for strongly nonlinear circuits, speeding up the HB runtimes by several times compared to using the frequency-domain block-diagonal preconditioner. Also, an approximate Galerkin HB formulation is derived, yielding a small improvement in accuracy over the standard pseudospectral HB formulation, and about a factor of 1.5 runtime speedup in runs reaching identical solution error. Next, we introduce and develop the Time-Mapped Harmonic Balance method (TMHB) as a fast Krylov-subspace spectral method that overcomes the inefficiency of standard harmonic balance for circuits with rapid transitions. TMHB features a non-uniform grid and a time-map function to resolve the sharp features in the signals. At the core of the TMHB method is the notion of pseudo Fourier approximations. The rapid transitions in the solution waveforms are well approximated with pseudo Fourier interpolants, whose building blocks are complex exponential basis functions with smoothly varying frequencies. The TMHB features a matrix-implicit Krylov-subspace solution approach of same complexity as the standard harmonic balance method. As the TMHB solution is computed in a pseudo domain, we give a procedure for computing the real Fourier coefficients of the solution, and we also detail the construction of the time-map function. The convergence properties of TMHB are analyzed and demonstrated on analytic waveforms. The success of TMHB is critically dependent on the selection of a non-uniform grid. Two grid selection strategies, direct and iterative, are introduced and studied. Both strategies are a priori schemes, and are designed to obey accuracy and stability requirements. Practical issues associated with their use are also addressed. Results of applying the TMHB method on several circuit examples demonstrate that the TMHB method achieves up to five orders of magnitude improvement in accuracy compared to the standard harmonic balance method. The solution error in TMHB decays exponentially faster than the standard HB method when the size of the Fourier basis increases linearly. The TMHB method is also up to six times faster than the standard harmonic balance method in reaching identical solution accuracy, and uses up to five times less computer memory. The TMHB runtime speedup factor and storage savings favorably increase for stricter accuracy requirements, making TMHB well suited for high accuracy simulations of large strongly nonlinear circuits with rapid transitions.by Ognen J. Nastov.Ph.D

Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

Detection of inter-turn faults in multi-phase ferrite-PM assisted synchronous reluctance machine

Inter-turn winding faults in five-phase ferrite-permanent magnet-assisted synchronous reluctance motors (fPMa-SynRMs) can lead to catastrophic consequences if not detected in a timely manner, since they can quickly progress into more severe short-circuit faults, such as coil-to-coil, phase-to-ground or phase-to-phase faults. This paper analyzes the feasibility of detecting such harmful faults in their early stage, with only one short-circuited turn, since there is a lack of works related to this topic in multi-phase fPMa-SynRMs. Two methods are tested for this purpose, the analysis of the spectral content of the zero-sequence voltage component (ZSVC) and the analysis of the stator current spectra, also known as motor current signature analysis (MCSA), which is a well-known fault diagnosis method. This paper compares the performance and sensitivity of both methods under different operating conditions. It is proven that inter-turn faults can be detected in the early stage, with the ZSVC providing more sensitivity than the MCSA method. It is also proven that the working conditions have little effect on the sensitivity of both methods. To conclude, this paper proposes two inter-turn fault indicators and the threshold values to detect such faults in the early stage, which are calculated from the spectral information of the ZSVC and the line currentsPeer ReviewedPostprint (published version

HIGH-PERFORMANCE SPECTRAL METHODS FOR COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS

Recent research shows that by leveraging the key spectral properties of eigenvalues and eigenvectors of graph Laplacians, more efficient algorithms can be developed for tackling many graph-related computing tasks. In this dissertation, spectral methods are utilized for achieving faster algorithms in the applications of very-large-scale integration (VLSI) computer-aided design (CAD) First, a scalable algorithmic framework is proposed for effective-resistance preserving spectral reduction of large undirected graphs. The proposed method allows computing much smaller graphs while preserving the key spectral (structural) properties of the original graph. Our framework is built upon the following three key components: a spectrum-preserving node aggregation and reduction scheme, a spectral graph sparsification framework with iterative edge weight scaling, as well as effective-resistance preserving post-scaling and iterative solution refinement schemes. We show that the resultant spectrally-reduced graphs can robustly preserve the first few nontrivial eigenvalues and eigenvectors of the original graph Laplacian and thus allow for developing highly-scalable spectral graph partitioning and circuit simulation algorithms. Based on the framework of the spectral graph reduction, a Sparsified graph-theoretic Algebraic Multigrid (SAMG) is proposed for solving large Symmetric Diagonally Dominant (SDD) matrices. The proposed SAMG framework allows efficient construction of nearly-linear sized graph Laplacians for coarse-level problems while maintaining good spectral approximation during the AMG setup phase by leveraging a scalable spectral graph sparsification engine. Our experimental results show that the proposed method can offer more scalable performance than existing graph-theoretic AMG solvers for solving large SDD matrices in integrated circuit (IC) simulations, 3D-IC thermal analysis, image processing, finite element analysis as well as data mining and machine learning applications. Finally, the spectral methods are applied to power grid and thermal integrity verification applications. This dissertation introduces a vectorless power grid and thermal integrity verification framework that allows computing worst-case voltage drop or thermal profiles across the entire chip under a set of local and global workload (power density) constraints. To address the computational challenges introduced by the large 3D mesh-structured thermal grids, we apply the spectral graph reduction approach for highly-scalable vectorless thermal (or power grids) verification of large chip designs. The effectiveness and efficiency of our approach have been demonstrated through extensive experiments

Quantitative Assessment of Flame Stability Through Image Processing and Spectral Analysis

This paper experimentally investigates two generalized methods, i.e., a simple universal index and oscillation frequency, for the quantitative assessment of flame stability at fossil-fuel-fired furnaces. The index is proposed to assess the stability of flame in terms of its color, geometry, and luminance. It is designed by combining up to seven characteristic parameters extracted from flame images. The oscillation frequency is derived from the spectral analysis of flame radiation signals. The measurements involved in these two methods do not require prior knowledge about fuel property, burner type, and other operation conditions. They can therefore be easily applied to flame stability assessment without costly and complex adaption. Experiments were carried out on a 9-MW heavy-oil-fired combustion test rig over a wide range of combustion conditions including variations in swirl vane position of the tertiary air, swirl vane position of the secondary air, and the ratio of the primary air to the total air. The impact of these burner parameters on the stability of heavy oil flames is investigated by using the index and oscillation frequency proposed. The experimental results obtained demonstrate the effectiveness of the methods and the importance of maintaining a stable flame for reduced NOx emissions. It is envisaged that such methods can be easily transferred to existing flame closed-circuit television systems and flame failure detectors in power stations for flame stability monitoring

Decoupling Bimolecular Recombination Mechanisms in Perovskite Thin Films Using Photoluminescence Quantum Yield

We present a novel analytical model for analysing the spectral photoluminescence quantum yield of non-planar semiconductor thin films. This model considers the escape probability of luminescence and is applied to triple-cation perovskite thin films with a 1-Sun photoluminescence quantum yield approaching 25%. By using our model, we can decouple the internal radiative, external radiative, and non-radiative bi-molecular recombination coefficients. Unlike other techniques that measure these coefficients separately, our proposed method circumvents experimental uncertainties by avoiding the need for multiple photoluminescence measurement techniques. We validate our model by comparing the extracted implied open-circuit voltage, effective luminescence escape probabilities, absorptivity, and absorption coefficient with values obtained using established methods and found that our results are consistent with previous findings. Next, we compare the implied 1-Sun radiative open-circuit voltage and radiative recombination current obtained from our method with literature values. We then convert the implied open-circuit voltage and implied radiative open-circuit voltage to the injection-dependent apparent-effective and apparent-radiative carrier lifetimes, which allow us to decouple the different recombination coefficients. Using this lifetime analysis, we predict the efficiency losses due to each recombination mechanism. Our proposed analytical model provides a reliable method for analysing the spectral photoluminescence quantum yield of semiconductor thin films, which will facilitate further research into the photovoltaic properties of these materials

Rapid mapping of digital integrated circuit logic gates via multi-spectral backside imaging

Modern semiconductor integrated circuits are increasingly fabricated at untrusted third party foundries. There now exist myriad security threats of malicious tampering at the hardware level and hence a clear and pressing need for new tools that enable rapid, robust and low-cost validation of circuit layouts. Optical backside imaging offers an attractive platform, but its limited resolution and throughput cannot cope with the nanoscale sizes of modern circuitry and the need to image over a large area. We propose and demonstrate a multi-spectral imaging approach to overcome these obstacles by identifying key circuit elements on the basis of their spectral response. This obviates the need to directly image the nanoscale components that define them, thereby relaxing resolution and spatial sampling requirements by 1 and 2 - 4 orders of magnitude respectively. Our results directly address critical security needs in the integrated circuit supply chain and highlight the potential of spectroscopic techniques to address fundamental resolution obstacles caused by the need to image ever shrinking feature sizes in semiconductor integrated circuits